Refraction and diffraction are two mechanisms by which optical effects are characterized. Diffraction theory concerns itself with the propagation of light. It is generally useful to consider the particular case of propagation through an aperture. The aperture may be an empty region defined simply by its boundary. Or it may be a region of optical material of varying thickness and/or varying refractive index, so as to selectively retard various portions of the incident wavefront. In any case, as light squeezes through such an aperture it is said to undergo `diffraction`.
Sometimes when light passes through an aperture, there is found to exist a point in space where the light seems to be concentrated or focussed. There exists a subset of these situations wherein this focal point can be calculated by use of a simple equation known as Snell's Law. These special cases occur when the optical material contained within the aperture is smoothly and very slowly varying, and the dimensions of the aperture are large. When all of this is true, light can be characterized as being propagated by the special case of diffraction that is called `refraction`.
However, because this situation is so common, refraction is often viewed to be a complete theory. But in the case where there are sharp cuts in a lens, the `smoothly varying` requirement is violated and the calculation of light propagation requires the more general theory of `diffraction`.
The term `refraction` would be used whenever circumstances involved only apertures with smoothly varying internal structures. The term `diffraction` would be used whenever circumstances involved apertures whose internal structures comprised sharp boundaries and abrupt changes in optical path lengths.
Even in the simple cases however, diffraction theory is used for an exact solution that would not be obtainable using refraction theory.
The operation of any lens can be explained by the laws and rules pertaining to diffraction whereas the laws and rules pertaining to refraction will not explain the operation of a phase zone plate in a carrier lens. A "phase zone plate" (as employed herein and in the claims) is a unitary optical region of a lens utilizing the combination of a zone plate and optical facets in the zones, said combination diffracts light to produce a specific wavefront which results in a specific intensity distribution of light at the various order (e.g., 0.sup.th, 1.sup.st, etc.) foci of the zone plate.
The Cohen patents [Allen L. Cohen, U.S. Pat. Nos. 4,210,391; 4,338,005; and 4,340,283 ("Cohen patents")] are directed to the use of phase zone plates in the optic zone of a carrier lens to achieve a multifocal effect. A lens that utilizes a phase zone plate in the optic zone of a carrier lens to achieve a useful multifocal effect is characterized herein and in the claims hereof to be a "Cohen lens design." The optical properties and utility of a Cohen lens design is explained in terms of the laws and rules relating to diffraction.
A Cohen lens design utilizes a phase zone plate design of concentric zones wherein the radii "r.sub.k " of the concentric zones are substantially proportional to .sqroot.k and the zones are cut so as to direct or diverge light to more than one focal point. This .sqroot.k spacing is unique to diffraction and there is no analogous spacing pattern that occurs in refractive lens design.
A phase zone plate which generates a multifocal image is a lens and can be used independent of a carrier lens for the purpose of magnification or minification. When a phase zone plate is placed in carrier lens, and it dominates the optic zone region of the carrier lens, it will control the relative brightness of the multiple images created by the lens device. In addition, such a phase zone plate that dominates the optic zone region of a carrier lens device will contribute to the quality and nature of the image at a given foci. The significance of such a phase zone plate is its ability to control the transmitted light to the various orders as evidenced by the various foci, the chromatic dispersion effects at the various orders and the reduction in intensity of the light at the various orders, reflecting efficiency loss inherent in a multifocal phase zone plate. For example, a divergent or convergent or plano lens will dictate the magnification or minification of the light transmission and a phase zone plate in the lens will control the relative intensity of light at various focal points, and in this respect will create foci at the higher orders. This is simply illustrated by lens devices utilizing a phase zone plate that is a Fresnel zone plate possessing zone spacing according to .sqroot.k with parabolically shaped echelettes (which means they exhibit a linear profile in r.sup.2 space) that have a depth that accord with the design wavelength; e.g., if the design wavelength is yellow light which measures 555 nanometers, then the physical depth (or optical path length) of the echelette will be about 0.00555 millimeters, according to the relationship .lambda./(.eta.'-.eta.) where .eta.'.perspectiveto.1.43, .eta..perspectiveto.1.33 and .lambda. is the design wavelength, in this case that of yellow light. This phase zone plate, regardless of whether the carrier power of the lens body is divergent or convergent or plano, will be a monofocal lens device for the design wavelength and will direct all of the light of the design wavelength to the first order focal point along the axial axis of the optic zone. This means that a user of the lens device will see only near objects and will not be able to see distant objects even though the carrier power of the lens would, in a smooth lens device relying on the mathematical relationships utilized in refraction, allow visual transmission of distant objects. The phase zone plate is directing the light by diverting it to the near focal point. The lens structurally is the carrier for the phase zone plate. In this case, the phase zone plate is dictating the direction in which light is transmitted and is determining visual precision at the various focal orders. Moreover, in a bifocal lens of the Cohen lens design, in which light is transmitted to the 0.sup.th order, the phase zone plate will contribute to the chromatic intensities at the 0.sup.th order of wavelengths other than the design wavelength. Though the image at the 0.sup.th order is not per se changed, it is affected by the phase zone plate. Regardless of the location of the 0.sup.th order with a lens utilizing a phase zone plate in the optic zone, all light going to the 0.sup.th order is transmitted through the phase zone plate, and thus is diffracted light.
From the preceding, there is demonstrated the fact that a smooth optic zone will direct light to only one focal power, i.e., the 0.sup.th order, and a phase zone plate optic zone, utilizing diffraction, can direct light to only one focal power, the 1.sup.st order. It is the dominating directional power of diffraction in this case which diverts the light to the 1.sup.st order. The Cohen lens design, in its uniqueness, utilizes diffraction to direct light to more than one focal power. It directs the light to more than one focal power by utilizing phase shifting by either (i) cutting into the phase zone plate to alter its thickness according to an appropriate scheme or (ii) altering the refractive index of the lens body at zones within the phase zone plate. By varying the inclination of the zones it is possible to vary, thus phase shift, the transmitted light.
The Cohen lens design employs, in one embodiment, alternating and inclined half-period zones which are termed odd and even zones to obtain a multifocal effect. Each such zone reduces the thickness of the carrier lens body by the degree of the inward inclination. This kind of inclination will optically phase shift the light being transmitted by the lens in a varying relationship. The more pronounced the variation in phase shifting, the more light is directed or diverted to the higher orders. If the inclination is relatively less, the variation in phase shifting is less and more of the transmitted light will be directed from the lens surface to lower order focal points. It is through these variations in inclination and the profile of the inclination that one may dictate the direction of diffracted light to more than one focal power.
The Cohen lens design also teaches variations in refractive index through the use of embedded materials in surfaces of the lens as another mechanism other than surface relief profile to control phase shifting.
The inclined zones of the Cohen lens design follow the principles of Fresnel zones as discussed by H. Ruhle, U.S. Pat. No. 3,004,470, patented Oct. 17, 1961, except that the Cohen lens design incorporates the .sqroot.k spacing. Ruhle shows that a stepped Fresnel parabolic lens zone is nothing more than a smooth version of stepped inclined pairs of surfaces.
In a multifocal phase zone plate of a Cohen lens design, the alternating odd and even zones provide variations in the optical path length to phase shift the transmitted light. These zones may reside within a full-period zone or exist through the use of multiple half-period zones. A full-period zone is defined by the smallest repetitive sequence of facets within a phase zone plate which are spaced substantially proportional to .sqroot.k. Such spacing is characterized by the formula: ##EQU1## where d represents the 1.sup.st order focal length and .lambda. is the design wavelength. A half-period zone, for the purposes of this invention, is characterized by the formula: ##EQU2##
A full-period zone in a phase zone plate is recognized as comprising a pair of alternating zones having half-period spacing. A full-period zone may contain noncontinuous blazing or continuous blazing. A full-period noncontinuous blazing constitutes an independent profile that contains a discontinuity usually at about the half-period thereof and a full-period continuous blazing constitutes an independent profile that is free of discontinuities that are in the form of steps, that is, it is continuous, over the width of the full-period. Since each half-period zone of a full-period zone differs to the extent that incident light of the design wavelength is phase shifted differently, each zone will contribute to the ingredients necessary to directing or diverting light to multiple focal points.
It has been pointed out in the prosecution of De Carle, U.S. Pat. No. 4,704,016, patented Nov. 3, 1987, that
"[T]he Fresnel zone plate or lens operates on the principle that adjacent zones pass light which is mutually out of phase by a half period so that if alternate zones are blacked out, the light passing through the plate and arriving at a point distant from the zone plate will be brighter than in the absence of the zone plate because destructive interference has been avoided. In order to achieve this effect, it can be shown mathematically that the radii bounding the zones are, to a first approximation, equal to: ##EQU3## where f=zone plate focal length, n=0, 1, 2, 3, 4. . . , and .lambda.=wavelength of the light. In the case of a zone plate having a power of, for example, 5 diopters, which is a typical power of ophthalmic lenses, the size of the first zone would be of the order 0.3 mm while the width of the eighth zone would be of the order of a few hundreths of a millimeter. The efficiency in terms of the sharpness of the image focused by the zone plate will increase with the number of zones so that for reasonable optical properties a plate with a large number of zones is desired."
Freeman and Stone, Transaction BCLA Conference 1987, page 15, utilize about 6 full-period zones for a +1 Diopter add. That would translate into 12 half-period zones.
Thus there has been a recognition by some skilled in the art that lenses of the Cohen lens design require a substantial number of zones to achieve a sharp image. However, lenses which necessitate the presence of such a large number of zones in a bifocal lens would deprive a significant number of people from the benefits of contact and intraocular lenses of the Cohen lens design.
There are many eye conditions which require special variations in the design of the phase zone plate of a Cohen lens design. For example, cataract patients are generally older in years and therefore have small pupils. In such cases, their treatment can involve the implantation of an intraocular lens (IOL). There are situations where it is desirable to use an IOL containing a bifocal phase zone plate. Because of the pupil reduction in such patients, the phase zone plate should be operative within a very small aperture to accommodate the size of the pupil. In addition, because of the placement of a phase zone plate IOL within the eye, the aperture stop would be reduced to about 85% of the apparent pupil size. Therefore, the phase zone plate should be operative in a region smaller than the iris size which is only 85% of the apparent pupil size.
There is the need for a bifocal contact or IOL optical device which solves the pupil reduction problem by providing a reasonable number of discontinuities within a small optic zone so as to accommodate a small pupil size such as exists in the case of cataract patients.